Cluster integrals and statistical mechanics of solutions

A formally convergent method for calculating the thermodynamic properties of solutions containing molecules not widely different in size and interaction energies is developed using the cluster-integral approach of the theory of imperfect gases. The potential energy of the actual solution is referred to the potential energy of a suitably chosen ‘reference liquid’; the correction terms which are required to give the correct energy for the solution give rise to cluster integrals which contain distribution functions of the reference liquid as factors in the integrand. Even if all the cluster integrals are neglected a useful result may be obtained. The first cluster integral, corresponding to the second virial coefficient in the theory of imperfect gases, is comparatively easy to evaluate. This approach provides a unified and formally exact basis for existing approximate theories of solutions, as well as a method for obtaining more accurate results.